Summary

At this time, as per our documentation

"Adding multiple ServiceNow integrations for different Opsgenie teams is not supported without code modification in Opsgenie ServiceNow application and configuration modification in Opsgenie." 

Suggestion

Add functionality to official support multiple integrations. 

Workaround

Customers who require this functionality must rewrite parts of the Opsgenie ServiceNow app to support multiple integrations. The code in “OpsGenie Web Svc Create” can be used as a starting point.